When the car isn't running, or when your lights are on, or your defogger, your car won't be at 14.4.
12.5 is a reasonable voltage with the engine off or with a heavier load.
The rest of your questions could fill a book.
Class D amplifiers initially did not sound as good as Class AB with mids and highs. Bass was fine. The consensus now is that current technology has eliminated the difference.
But you have the "all amps sound alike" school and the "all amps have their own signature sound" school.
You won't navigate those polar extremes in a forum like this.
Distortions differ in type and spectral distribution. Harmonic, intermodulation, odd-order, even-order...
The baseline for a high-fidelity amplifier is to be flat from 20 to 20k, with less than 3dB of deviation (much less).
My approach is that power, noise rejection, and dynamic headroom are the most important aspects for car audio. A Class AB amp with more dynamic headroom sounds better than a Class D amp without dynamic headroom - even with the same RMS power rating.